Let A be a set and R and S be relations on A. Dene the relation R + S on A by R + S = (R-S) [ (S-R): Show that: (a) If A is countable, then so does R + S. (b) Show that the converse does not hold; that is, give an example of a set A that is uncountable but R + S is countable. (c) Prove or disprove: If R and S are partial orders on A, then so does R + S.
Let A be a set and R and S be relations on A. Dene the relation R + S on A by R + S = (R-S) [ (S-R): Show that: (a) If A is countable, then so does R + S. (b) Show that the converse does not hold; that is, give an example of a set A that is uncountable but R + S is countable. (c) Prove or disprove: If R and S are partial orders on A, then so does R + S.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let A be a set and R and S be relations on A. Dene the relation R + S on A by
R + S = (R-S) [ (S-R):
Show that:
(a) If A is countable, then so does R + S.
(b) Show that the converse does not hold; that is, give an example of a set A that is uncountable
but R + S is countable.
(c) Prove or disprove: If R and S are partial orders on A, then so does R + S.
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